Refraction at plane surface

```Refraction at plane surface and
Prisms
Dr. M K Raghavendra
BASE, Bangalore
Type 1 – Snell’s law and RI
Snell’s law:
1 n2 
sin(i )
sin(r )
c
Absolute R I in terms
n
of speed of light
v
Modified Snell’s law
n1 sin i1  n2 sin i2
V  Y  R
nV  nY  nR
1 n2 
Relative R I in terms
of speed of light
Relative R I in terms
of absolute R I
v1
v2
n2
1 n2 
n1
Relative R I in terms of
wavelength of light
1 n2 
Frequency remains constant
1
2
1) A ray of light is incident on the interface of two media at
an angle of 450 and is refracted in to the other medium
at an angle of 300. If the speed of light in the first
medium is 3X108ms-1 ,what is the speed of light in the
second medium?
(1) 1.96X108ms-1
(2) 2.12X108ms-1
(3) 3.18X108ms-1
(4) 3.33X108ms-1
Snell’s law: n  sin(i )
sin(r )
sin 45 3X 10 8

sin 30
v
1/ 2 3X 10 8

1/2
v
3X 10 8
v
 2.12 X 10 8 ms 1
2
c
n
v
Thus sin(i )
c
sin(r ) v
In general
sin i1 v1

sin i2 v2

2)A ray of light is travelling from medium A to medium B. The angle of incidence is i
and that of refraction is r. Graph between sin(i) and sin(r) is as shown in Figure below.
We can conclude the following
(i) Speed of light in medium B is three-fourth of that in medium A.
(ii) Total internal reflection cannot take place.
(iii) Refractive index of medium B is greater than that of medium A.
sin (r)
O
Correct conclusions are
(1) Only (i) and (ii)
(3) (i), (ii) and (iii)
370
sin (i)
(2) Only (ii) and (iii)
(4) Only (i) and (iii)
sin r
The slope of the straight line:
 tan 
sin i
sin (r)
sin (r)
O
370
sin (i)
sin (i)
sin r vB 3


sin i v A 4
3
vB  v A
4
sin r
 tan 37 0
sin i
sin r 3
or

sin i 4
Medium B is denser than medium A
Since nb > na TIR cannot take place
3) Given refractive index of glass with respect to air is ang
= 3/2 and that of water with respect to air is anw = 4/3,
the refractive index of glass with respect to water is
(1) 8/9
(2) 9/8
(3) 2
(4) 1/2
n1
1 n2 
n2
a
ng 
ng
na
ng
and
ng /na
nw
a nw 
na
3/2 9



w ng 
nw nw /na 4/3 8
Type 2: Normal Shift and Lateral Shift
Lateral shift
SL 
Normal shift
a) Object in denser
b) Object in rarer
t sin( i  r )
cos r
1
SN  t(1 
)
r nd
SV  SY  SR
r nd 
SN  t(n  1)
SV  SY  SR
Re al depth
Apparent depth
r nd 
Apparent depth
Real depth
4) A vessel of height h is filled with a liquid of refractive
index n1 to a height h/2 and the upper half of the vessel
is filled with a liquid of refractive index n2. The apparent
depth of the vessel as seen along the normal is
1)
 n1 n 2 
h

n

n
2 
 1
3)
h  n1  n 2 


2  n1n 2 
2)
h
2
 n1 n 2 


n

n
2 
 1
4)
2
h
 n1n 2 


n

n
2
 1
In case of one liquid the apparent depth is given by
In case of many layers of liquid
A.D 
h /2 h /2

n1
n2
h  n  n1 
=  2

2  n1 n2 
ti
A.D  
ni
real depth
refractive index
5) A ray of light passes through four transparent media with refractive
indices 1 2 3 and 4 as shown in the figure. The surfaces of all
media are parallel. If the emergent ray CD is parallel to the incident
ray AB, we must have
(1)
(2)
(3)
(4)
1=
2
2=
3
3=
4
4=
1
1
2
B
A
D
3
C
4
a sin ia  b sin ib
1 sin i1  4 sin i4
Apply to medium 1 and medium 4
Since ray AB and CD are parallel, i1 and i4 are equal
Implies
1
=
4
In genral
a sin ia  b sin ib  c sin ic ...............
6) An ink dot on a paper placed on a table top is viewed from a
distance of 30 cm above it with the help of a telescope. A 16 cm thick
glass slab is placed on the ink dot. By what distance the telescope
should be raised to refocus the ink dot ? The refractive index of glass is
1.6.
(1)
(2)
(3)
(4)
3 cm
4 cm
5 cm
6 cm
The telescope should be moved up by a distance (y) equal to normal
shift produced by the slab
1

Sn  t  1  
n

1 

y  Sn  16  1 
  6cm
1.6 

7) Consider the situation shown in the figure. The bottom of the vessel
is a plane mirror, S is a small fish located at a height of H/2 from the
plane of the mirror, T is a human eye located at a height of H from the
surface of water. The distances at which the fish sees the images of the
eye (with respect to its position) are
1)
T
1
3


H  2n   aboveand H  2n   below
2
2


2)
1 
3 


H 1   aboveand H 1   below
 2n 
 2n 
3)
1
3


H  n   aboveand H  n   below
2
2


4)
2 
3 


H  2   aboveand H  2   below
2n 
2n 


H
H
S
(H/2)
Image 1
nH + H/2
T
nH + H
H
Image 1: H (n+1/2)
A.P = nH
H
S
nH + H+H/2
(
H/2)
Image 2: H (n+3/2)
Image 2
Type 3: Critical angle and Total Internal Reflection
nr
sin C 
nd
1
sin C 
r nd
nV  nY  nR
CV  CY  C R
vd
sin C 
vr
8) A, B and C are three optical media of respective critical angles C1,
C2 and C3. Total internal reflection of light can occur from A to B
and also from B to C but not from C to A. Then the correct relation
between critical angles is
(1)C1>C2>C3
(2) C1= C2= C3
(3)C3> C1> C2
(4)C1<C2<C3
T I R can occur when light travels from medium A to medium B
 nA  nB
T I R can occur when light travels from medium B to medium C
 nB  nC
Therefore
nA  nB  nC
 C1  C2  C3
9) What is the critical angle, C for calcite ( =1.5) immersed
in oil ( =1.1)?
(1)
C  tan11.1 1.5
(2)
C  cos11.1 1.5
(3)
C  sin 11.5 1.1
(4)
C  sin 11.1 1.5
nO
1
sin C 

nC
O nC
1.1
sin C 
1.5
Type 4: Prism, angle of deviation, minimum deviation
d  i1  i2  A
A  r1  r2
n
AD
2
A
sin
2
sin
10) The minimum angle of deviation for a prism of
refractive index 1.732 is equal to its refracting angle.
What is the angle of prism?
(1) 400
(2) 450
(3) 600
(4) 300
In this case A = D
AD
sin(
)
2
n
A
sin( )
2
A A
sin(
)
sin A
2
1.732 

A
A
sin( )
sin
2
2
A
A
2 sin cos
sin A
A
2
2
3

 2 cos
A
A
2
sin
sin
2
2
A/2 =300
3
A
 cos
o
2
2
Or A=60
11) A ray of light is incident on one refracting face of a prism
of angle 750. It passes through the prism and is incident on
the other face at critical angle. If the refractive index of the
material of the prism is √2, then the angle of incidence on
the first face is
(1) 300
(2) 450
(3) 600
(4) 75 0
sin C 
1
1

n
2
We know that
C = 450
r1 + C =750
r1 =300
750
r1 C
sin i
but n 
sin r
sin i
2
0
sin 30
1
1
sin i  2 X 
2
2
i  450
Type 5: Small angled prism , angular dispersion and dispersive power
Deviation
d  A(n  1)
Angular dispersion
  A(nV  nR )
Dispersive power
In case of C D F line
angular dispersion
nV  nR


nv  nR
mean deviation
1
2
nmean 
nF  nC
 nD
2
12) The dispersive power of the material of the prism for
which refractive index for violet and red colours are nv =
1.524, nr = 1.514 respectively is
(1)
(2)
(3)
(4)
0.025
0.034
0.019
0.015
Dispersive power  is given by
angular dispersion

net deviation
(nV  nR )

nV  nR
1
2
(1.524  1.514)
0.01


 0.019
1.524  1.514
 1 0.519
2
Type 6: Combination of Prisms
Dispersion with out deviation
A(nD  1)   A(nD  1)
  A(nd  1)(1 
Deviation with out dispersion

)

A(nF  nC )   A(nF  nC )
d  A(nD  1)  A(nD  1)
13) A crown glass prism of 60 is cemented with a flint glass prism to
form a pair which produces dispersion without deviation. If the
refractive index of the crown glass prism is 1.52 and that of flint
glass 1.66, then the angle of flint glass pair should be
(1) 4.730
(2) 5.730
(3) 6.730
(4) 7.730
Condition for dispersion with out deviation is
A1 (ny  1)  A2 (ny1  1)
6(1.52  1)   A2 (1.66  1)
6X 0.52
A2 
 4.72
0.66
Conceptual questions
14) Light appears to travel in straight line because
(1)The frequency of light is very small
(2) Light consists of very small particles
(3) The wavelength of light is very small
(4) The velocity of light is different for different colours.
15) When light is refracted through a prism, maximum
deviation occurs when the following conditions are satisfied
(i) the ray is incident grazing the first face
(ii) the ray emerges out grazing its second face
Options
(1) Only in case (i)
(3) In both the cases
(2) Only in case (ii)
(4) Not under these cases
16) A man is swimming underwater with undisturbed
surface. Looking up at a bright sky through the water, he will
see
(1)a bright patch directly above whose angular size is
independent of the depth of the swimmer
(2)a shining surface of the water
(3) just darkness
(4) a bright patch directly above whose angular size depends
upon the depth of the swimmer
CC
All the best
Thank You
```